C:\Users\SINDH\AppData\Local\Temp\ipykernel_12840\2782822628.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Price"].replace("?", np.nan, inplace = True)

dtype('float64')

<Axes: xlabel='drive-wheels', ylabel='Price'>

Text(0, 0.5, 'Price')

C:\Users\SINDH\AppData\Local\Temp\ipykernel_12840\878192950.py:3: MatplotlibDeprecationWarning: Getting the array from a PolyQuadMesh will return the full array in the future (uncompressed). To get this behavior now set the PolyQuadMesh with a 2D array .set_array(data2d).
  plt.colorbar()

C:\Users\SINDH\AppData\Local\Temp\ipykernel_12840\2475278966.py:3: MatplotlibDeprecationWarning: Getting the array from a PolyQuadMesh will return the full array in the future (uncompressed). To get this behavior now set the PolyQuadMesh with a 2D array .set_array(data2d).
  plt.colorbar()

Text(0.5, 1.0, 'Correlation b/w Engine Size and Price')

Text(0.5, 1.0, 'Negative Correlation b/w highway-mpg and Price')

C:\Users\SINDH\AppData\Local\Temp\ipykernel_12840\3306160387.py:2: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["horsepower"].replace("?", 0, inplace = True)
C:\Users\SINDH\AppData\Local\Temp\ipykernel_12840\3306160387.py:4: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["horsepower"].fillna(0, inplace = True)
C:\Users\SINDH\AppData\Local\Temp\ipykernel_12840\3306160387.py:5: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Price"].fillna(0, inplace = True)

0.6912878787942788

1.8175735366187578e-30

0      27
1      27
2      26
3      30
4      22
       ..
200    28
201    25
202    23
203    27
204    25
Name: highway-mpg, Length: 205, dtype: int64

0

dtype('O')

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10120\2913407292.py:2: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Price"].replace("?", np.nan, inplace = True)

4

0

0      13495.0
1      16500.0
2      16500.0
3      13950.0
4      17450.0
        ...   
200    16845.0
201    19045.0
202    21485.0
203    22470.0
204    22625.0
Name: Price, Length: 201, dtype: float64

LinearRegression()

LinearRegression()

c_0 =  38423.3058581574
c_1 =  [-821.73337832]

C:\Users\SINDH\AppData\Roaming\Python\Python312\site-packages\sklearn\base.py:493: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(

array([26097.30518333])

horsepower     object
curb-weight     int64
engine-size     int64
highway-mpg     int64
dtype: object

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10120\2628235679.py:2: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["horsepower"].replace("?", np.nan, inplace = True)

2

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10120\3197711793.py:3: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["horsepower"].replace(np.nan, ave_hp, inplace = True)

0

0
0
0
0

LinearRegression()

LinearRegression()

c_0 =  -15824.038208234477
c_{1-4} =  [53.61042729  4.70886444 81.47225667 36.39637823]

C:\Users\SINDH\AppData\Roaming\Python\Python312\site-packages\sklearn\base.py:493: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(

array([87642.15866469])

11976801.681229591

(20640, 3)

<Axes: xlabel='longitude', ylabel='latitude'>

KMeans(n_clusters=3, random_state=0)

KMeans(n_clusters=3, random_state=0)

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: ylabel='median_house_value'>

0.7499115323584772

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: >

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: ylabel='median_house_value'>

C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\245617363.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  selected_features["housing_median_age"].replace("?", np.nan, inplace = True)
C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\245617363.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  selected_features["housing_median_age"].replace("?", np.nan, inplace = True)

0

C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\668685475.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  selected_features["total_rooms"].replace("?", np.nan, inplace = True)
C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\668685475.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  selected_features["total_rooms"].replace("?", np.nan, inplace = True)

0

C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\344786479.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  selected_features["total_bedrooms"].replace("?", np.nan, inplace= True)
C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\344786479.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  selected_features["total_bedrooms"].replace("?", np.nan, inplace= True)

207

C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\2879441710.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  selected_features["population"].replace("?", np.nan, inplace = True)
C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\2879441710.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  selected_features["population"].replace("?", np.nan, inplace = True)

0

C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\3851724696.py:2: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  selected_features["total_bedrooms"].replace(np.nan, selected_features_mean, inplace= True)
C:\Users\SINDH\AppData\Local\Temp\ipykernel_1252\3851724696.py:2: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  selected_features["total_bedrooms"].replace(np.nan, selected_features_mean, inplace= True)

0

population
3.0           6.00
5.0           3.00
6.0           2.00
8.0           3.25
9.0           7.00
            ...   
15507.0    5290.00
16122.0    5471.00
16305.0    6210.00
28566.0    6445.00
35682.0    4819.00
Name: total_bedrooms, Length: 3888, dtype: float64

[[0.04330435 0.92945912 0.13625026 0.34009754]
 [0.00277219 0.93713188 0.14600195 0.3169536 ]
 [0.03331069 0.93974594 0.12171215 0.31773278]
 ...
 [0.00675685 0.89587898 0.19276899 0.40024407]
 [0.008808   0.91016017 0.20013737 0.36259607]
 [0.00504461 0.87807691 0.19421737 0.43730437]]

array([[ 0.63157895, -0.73342156, -0.89241877, -0.89978678],
       [-0.42105263,  2.92427584,  1.92924188,  1.31663113],
       [ 1.21052632, -0.38817821, -0.71624549, -0.71428571],
       ...,
       [-0.63157895,  0.0746949 ,  0.13574007, -0.16950959],
       [-0.57894737, -0.15703573, -0.08375451, -0.45309168],
       [-0.68421053,  0.38700191,  0.51407942,  0.23560768]])

array([[ 0.39606755, -0.45993376, -0.55964202, -0.56426255],
       [-0.11179811,  0.77645525,  0.51225331,  0.34959258],
       [ 0.74513076, -0.2389403 , -0.44087975, -0.43967343],
       ...,
       [-0.93980159,  0.11114744,  0.20198383, -0.25223353],
       [-0.76539427, -0.20760825, -0.11072721, -0.59900744],
       [-0.70657304,  0.39965056,  0.53088143,  0.2433082 ]])

KMeans(n_clusters=4, random_state=0)

KMeans(n_clusters=4, random_state=0)

<Axes: xlabel='PC1', ylabel='PC2'>

<Axes: xlabel='PC1', ylabel='PC2'>

<Axes: ylabel='PC1'>

0.5273664489203738

0

Area                0
Bedrooms            0
Bathrooms           0
Stories             0
Mainroad            0
Parking             0
Furnishingstatus    0
Price               0
dtype: int64

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\1078061793.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Area"].replace("?", np.nan, inplace = True)

9

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\2500254421.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Bedrooms"].replace("?", np.nan, inplace = True)

dtype('float64')

7

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\2709543407.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Bathrooms"].replace("?", np.nan, inplace = True)

5

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\1854985383.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Stories"].replace("?", np.nan, inplace = True)

7

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\959753586.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Mainroad"].replace("?", np.nan, inplace = True)

0

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\1665768048.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Parking"].replace("?", np.nan, inplace = True)

6

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\2512529072.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Furnishingstatus"].replace("?", np.nan, inplace = True)

0

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\2782822628.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Price"].replace("?", np.nan, inplace = True)

3

0      13300000.0
1      12250000.0
2      12250000.0
3      12215000.0
4      11410000.0
          ...    
540     1820000.0
541     1767150.0
542     1750000.0
543     1750000.0
544     1750000.0
Name: Price, Length: 542, dtype: float64

0      7420.0
1      8960.0
2         NaN
3      7500.0
4      7420.0
        ...  
540    3000.0
541    2400.0
542    3620.0
543    2910.0
544    3850.0
Name: Area, Length: 542, dtype: float64

3

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\2436856013.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Bedrooms"].replace(np.nan, mean_bedrooms, inplace=True)

2

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\3660585759.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Bathrooms"].replace(np.nan, mean_bathrooms, inplace=True)

2

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\1488270682.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Stories"].replace(np.nan, mean_stories, inplace = True)

1

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10144\243805928.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Parking"].replace(np.nan, mean_parking, inplace=True)

['yes' 'no']

['furnished' 'semi-furnished' 'unfurnished']

Mainroad
yes    465
no      77
Name: count, dtype: int64

Furnishingstatus
semi-furnished    226
unfurnished       178
furnished         138
Name: count, dtype: int64

            Area  Bedrooms  Bathrooms  Stories  Parking       Price  \
0    7420.000000       4.0        2.0      3.0      2.0  13300000.0   
1    8960.000000       3.0        4.0      4.0      3.0  12250000.0   
2    5155.748593       3.0        2.0      2.0      2.0  12250000.0   
3    7500.000000       4.0        2.0      2.0      3.0  12215000.0   
4    7420.000000       4.0        1.0      2.0      2.0  11410000.0   
..           ...       ...        ...      ...      ...         ...   
540  3000.000000       2.0        1.0      1.0      2.0   1820000.0   
541  2400.000000       3.0        1.0      1.0      0.0   1767150.0   
542  3620.000000       2.0        1.0      1.0      0.0   1750000.0   
543  2910.000000       3.0        1.0      1.0      0.0   1750000.0   
544  3850.000000       3.0        1.0      2.0      0.0   1750000.0   

     Mainroad_no  Mainroad_yes  Furnishingstatus_furnished  \
0          False          True                        True   
1          False          True                        True   
2          False          True                       False   
3          False          True                        True   
4          False          True                        True   
..           ...           ...                         ...   
540        False          True                       False   
541         True         False                       False   
542        False          True                       False   
543         True         False                        True   
544        False          True                       False   

     Furnishingstatus_semi-furnished  Furnishingstatus_unfurnished  
0                              False                         False  
1                              False                         False  
2                               True                         False  
3                              False                         False  
4                              False                         False  
..                               ...                           ...  
540                            False                          True  
541                             True                         False  
542                            False                          True  
543                            False                         False  
544                            False                          True  

[542 rows x 11 columns]

0       True
1       True
2      False
3       True
4       True
       ...  
540    False
541    False
542    False
543     True
544    False
Name: Furnishingstatus_furnished, Length: 542, dtype: bool

0
0
0
0
0
0
0
0
0
0
0

LinearRegression()

LinearRegression()

c_0 =  -55069.20985339861
c_{1-4} =  [ 2.76303444e+02  2.02463933e+05  1.12200914e+06  4.96912078e+05
  3.47723155e+05 -3.03209898e+05  3.03209898e+05  2.70695767e+05
  6.91308081e+04 -3.39826575e+05]

C:\Users\SINDH\AppData\Roaming\Python\Python312\site-packages\sklearn\base.py:493: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(

array([7809064.56773169])

1472162563248.0195

(0.0, 13877500.0)

<Axes: xlabel='Bedrooms', ylabel='Price'>

<Axes: xlabel='Area', ylabel='Price'>

Patient ID         object
Age                 int64
BMI               float64
Diagnosis          object
Blood Pressure     object
dtype: object

Patient ID         0
Age                0
BMI               14
Diagnosis          9
Blood Pressure     9
dtype: int64

C:\Users\SINDH\AppData\Local\Temp\ipykernel_10184\4099862312.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["BMI"].replace(np.nan, mean, inplace = True)

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[11], line 1
----> 1 mean_bp = df["Blood Pressure"].mean()

File ~\AppData\Roaming\Python\Python312\site-packages\pandas\core\series.py:6529, in Series.mean(self, axis, skipna, numeric_only, **kwargs)
   6521 @doc(make_doc("mean", ndim=1))
   6522 def mean(
   6523     self,
   (...)
   6527     **kwargs,
   6528 ):
-> 6529     return NDFrame.mean(self, axis, skipna, numeric_only, **kwargs)

File ~\AppData\Roaming\Python\Python312\site-packages\pandas\core\generic.py:12413, in NDFrame.mean(self, axis, skipna, numeric_only, **kwargs)
  12406 def mean(
  12407     self,
  12408     axis: Axis | None = 0,
   (...)
  12411     **kwargs,
  12412 ) -> Series | float:
> 12413     return self._stat_function(
  12414         "mean", nanops.nanmean, axis, skipna, numeric_only, **kwargs
  12415     )

File ~\AppData\Roaming\Python\Python312\site-packages\pandas\core\generic.py:12370, in NDFrame._stat_function(self, name, func, axis, skipna, numeric_only, **kwargs)
  12366 nv.validate_func(name, (), kwargs)
  12368 validate_bool_kwarg(skipna, "skipna", none_allowed=False)
> 12370 return self._reduce(
  12371     func, name=name, axis=axis, skipna=skipna, numeric_only=numeric_only
  12372 )

File ~\AppData\Roaming\Python\Python312\site-packages\pandas\core\series.py:6437, in Series._reduce(self, op, name, axis, skipna, numeric_only, filter_type, **kwds)
   6432     # GH#47500 - change to TypeError to match other methods
   6433     raise TypeError(
   6434         f"Series.{name} does not allow {kwd_name}={numeric_only} "
   6435         "with non-numeric dtypes."
   6436     )
-> 6437 return op(delegate, skipna=skipna, **kwds)

File ~\AppData\Roaming\Python\Python312\site-packages\pandas\core\nanops.py:147, in bottleneck_switch.__call__.<locals>.f(values, axis, skipna, **kwds)
    145         result = alt(values, axis=axis, skipna=skipna, **kwds)
    146 else:
--> 147     result = alt(values, axis=axis, skipna=skipna, **kwds)
    149 return result

File ~\AppData\Roaming\Python\Python312\site-packages\pandas\core\nanops.py:404, in _datetimelike_compat.<locals>.new_func(values, axis, skipna, mask, **kwargs)
    401 if datetimelike and mask is None:
    402     mask = isna(values)
--> 404 result = func(values, axis=axis, skipna=skipna, mask=mask, **kwargs)
    406 if datetimelike:
    407     result = _wrap_results(result, orig_values.dtype, fill_value=iNaT)

File ~\AppData\Roaming\Python\Python312\site-packages\pandas\core\nanops.py:719, in nanmean(values, axis, skipna, mask)
    716     dtype_count = dtype
    718 count = _get_counts(values.shape, mask, axis, dtype=dtype_count)
--> 719 the_sum = values.sum(axis, dtype=dtype_sum)
    720 the_sum = _ensure_numeric(the_sum)
    722 if axis is not None and getattr(the_sum, "ndim", False):

File ~\AppData\Roaming\Python\Python312\site-packages\numpy\core\_methods.py:49, in _sum(a, axis, dtype, out, keepdims, initial, where)
     47 def _sum(a, axis=None, dtype=None, out=None, keepdims=False,
     48          initial=_NoValue, where=True):
---> 49     return umr_sum(a, axis, dtype, out, keepdims, initial, where)

TypeError: can only concatenate str (not "int") to str

dtype('O')

dtype('O')

0     23.416480
1     30.539825
2     31.654859
3     27.203652
4     27.203652
5     27.203652
6     20.154990
7     21.675982
8     31.285261
9     33.454012
10    27.203652
11    27.203652
12    27.203652
13    31.369513
14    27.203652
15    27.203652
16    27.203652
17    26.752736
18    27.885888
19    29.278378
20    23.506374
21    27.203652
22    29.850859
23    27.203652
24    27.203652
25    27.203652
26    23.628654
27    22.254053
28    28.550565
29    27.203652
Name: BMI, dtype: float64

0     0.245243
1     0.780872
2     0.864715
3     0.530014
4     0.530014
5     0.530014
6     0.000000
7     0.114369
8     0.836924
9     1.000000
10    0.530014
11    0.530014
12    0.530014
13    0.843259
14    0.530014
15    0.530014
16    0.530014
17    0.496108
18    0.581313
19    0.686019
20    0.252002
21    0.530014
22    0.729066
23    0.530014
24    0.530014
25    0.530014
26    0.261197
27    0.157836
28    0.631293
29    0.530014
Name: BMI, dtype: float64

1.0 0.0

array([21., 37., 53., 69.])

0     Old Home Age
1           Mature
2     Old Home Age
3           Adults
4           Mature
5           Adults
6           Adults
7           Mature
8           Mature
9           Adults
10    Old Home Age
11          Adults
12          Mature
13          Mature
14          Adults
15          Adults
16    Old Home Age
17          Mature
18          Adults
19          Mature
20    Old Home Age
21    Old Home Age
22          Mature
23          Mature
24          Adults
25          Mature
26    Old Home Age
27          Mature
28          Mature
29    Old Home Age
Name: Age-binned, dtype: category
Categories (3, object): ['Adults' < 'Mature' < 'Old Home Age']

(20640, 3)

<Axes: xlabel='longitude', ylabel='latitude'>

KMeans(n_clusters=3, n_init='auto', random_state=0)

KMeans(n_clusters=3, n_init='auto', random_state=0)

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: ylabel='median_house_value'>

0.7761558886704949

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: >

<Axes: xlabel='longitude', ylabel='latitude'>

<Axes: ylabel='median_house_value'>

C:\Users\SINDH\AppData\Local\Temp\ipykernel_8148\4080736814.py:1: DeprecationWarning: 
Pyarrow will become a required dependency of pandas in the next major release of pandas (pandas 3.0),
(to allow more performant data types, such as the Arrow string type, and better interoperability with other libraries)
but was not found to be installed on your system.
If this would cause problems for you,
please provide us feedback at https://github.com/pandas-dev/pandas/issues/54466
        
  import pandas as pd

symboling              int64
normalized-losses     object
make                  object
fuel-type             object
aspiration            object
num-of-doors          object
body-style            object
drive-wheels          object
engine-location       object
wheel-base           float64
length               float64
width                float64
height               float64
curb-weight            int64
engine-type           object
num-of-cylinders      object
engine-size            int64
fuel-system           object
bore                  object
stroke                object
compression-ratio    float64
horsepower            object
peak-rpm              object
city-mpg               int64
highway-mpg            int64
Price                 object
dtype: object

0        ?
1        ?
2        ?
3      164
4      164
      ... 
200     95
201     95
202     95
203     95
204     95
Name: normalized-losses, Length: 205, dtype: object

0        NaN
1        NaN
2        NaN
3      164.0
4      164.0
       ...  
200     95.0
201     95.0
202     95.0
203     95.0
204     95.0
Name: normalized-losses, Length: 205, dtype: float64

122.0

0      122.0
1      122.0
2      122.0
3      164.0
4      164.0
       ...  
200     95.0
201     95.0
202     95.0
203     95.0
204     95.0
Name: normalized-losses, Length: 205, dtype: float64

dtype('float64')

make
alfa-romero      122.000000
audi             144.285714
bmw              156.000000
chevrolet        100.000000
dodge            133.444444
honda            103.000000
isuzu            122.000000
jaguar           129.666667
mazda            123.705882
mercedes-benz    110.000000
mercury          122.000000
mitsubishi       140.615385
nissan           135.166667
peugot           146.818182
plymouth         128.000000
porsche          134.800000
renault          122.000000
saab             127.000000
subaru            92.250000
toyota           110.656250
volkswagen       121.500000
volvo             91.454545
Name: normalized-losses, dtype: float64

dtype('float64')

0       88.6
1       88.6
2       94.5
3       99.8
4       99.4
       ...  
200    109.1
201    109.1
202    109.1
203    109.1
204    109.1
Name: wheel-base, Length: 205, dtype: float64

0      21
1      21
2      19
3      24
4      18
       ..
200    23
201    19
202    18
203    26
204    19
Name: city-mpg, Length: 205, dtype: int64

0      11.190476
1      11.190476
2      12.368421
3       9.791667
4      13.055556
         ...    
200    10.217391
201    12.368421
202    13.055556
203     9.038462
204    12.368421
Name: city-mpg, Length: 205, dtype: float64

0      11.190476
1      11.190476
2      12.368421
3       9.791667
4      13.055556
         ...    
200    10.217391
201    12.368421
202    13.055556
203     9.038462
204    12.368421
Name: c-L/100Km, Length: 205, dtype: float64

dtype('O')

C:\Users\SINDH\AppData\Local\Temp\ipykernel_3076\2782822628.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.
The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.

For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.


  df["Price"].replace("?", np.nan, inplace = True)

0      13495.0
1      16500.0
2      16500.0
3      13950.0
4      17450.0
        ...   
200    16845.0
201    19045.0
202    21485.0
203    22470.0
204    22625.0
Name: Price, Length: 205, dtype: float64

dtype('float64')

0       8.703704
1       8.703704
2       9.038462
3       7.833333
4      10.681818
         ...    
200     8.392857
201     9.400000
202    10.217391
203     8.703704
204     9.400000
Name: h-L/100Km, Length: 205, dtype: float64

0      168.8
1      168.8
2      171.2
3      176.6
4      176.6
       ...  
200    188.8
201    188.8
202    188.8
203    188.8
204    188.8
Name: length, Length: 205, dtype: float64

0      0.811148
1      0.811148
2      0.822681
3      0.848630
4      0.848630
         ...   
200    0.907256
201    0.907256
202    0.907256
203    0.907256
204    0.907256
Name: length, Length: 205, dtype: float64

1.0

0      64.1
1      64.1
2      65.5
3      66.2
4      66.4
       ... 
200    68.9
201    68.8
202    68.9
203    68.9
204    68.9
Name: width, Length: 205, dtype: float64

60.3 72.3

0      0.316667
1      0.316667
2      0.433333
3      0.491667
4      0.508333
         ...   
200    0.716667
201    0.708333
202    0.716667
203    0.716667
204    0.716667
Name: width, Length: 205, dtype: float64

1.0

0.0

0     -2.015483
1     -2.015483
2     -0.542200
3      0.235366
4      0.235366
         ...   
200    0.726460
201    0.726460
202    0.726460
203    0.726460
204    0.726460
Name: height, Length: 205, dtype: float64 -2.4247287815509493 2.486215399755926

-2.4247287815509493

dtype('O')

'?'

0      13495
1      16500
2      16500
3      13950
4      17450
       ...  
200    16845
201    19045
202    21485
203    22470
204    22625
Name: Price, Length: 205, dtype: object

0      0.316667
1      0.316667
2      0.433333
3      0.491667
4      0.508333
         ...   
200    0.716667
201    0.708333
202    0.716667
203    0.716667
204    0.716667
Name: width, Length: 205, dtype: float64

---------------------------------------------------------------------------
UFuncTypeError                            Traceback (most recent call last)
Cell In[54], line 1
----> 1 bins = np.linspace(min(df["Price"]), max(df["Price"]), 4)

File ~\AppData\Roaming\Python\Python312\site-packages\numpy\core\function_base.py:129, in linspace(start, stop, num, endpoint, retstep, dtype, axis)
    125 div = (num - 1) if endpoint else num
    127 # Convert float/complex array scalars to float, gh-3504
    128 # and make sure one can use variables that have an __array_interface__, gh-6634
--> 129 start = asanyarray(start) * 1.0
    130 stop  = asanyarray(stop)  * 1.0
    132 dt = result_type(start, stop, float(num))

UFuncTypeError: ufunc 'multiply' did not contain a loop with signature matching types (dtype('<U5'), dtype('float64')) -> None

array([0.        , 0.33333333, 0.66666667, 1.        ])

	drive-wheels	body-style	Price
0	4wd	hatchback	7603.000000
1	4wd	sedan	12647.333333
2	4wd	wagon	9095.750000
3	fwd	convertible	11595.000000
4	fwd	hardtop	8249.000000
5	fwd	hatchback	8396.387755
6	fwd	sedan	9811.800000
7	fwd	wagon	9997.333333
8	rwd	convertible	23949.600000
9	rwd	hardtop	24202.714286
10	rwd	hatchback	14337.777778
11	rwd	sedan	21711.833333
12	rwd	wagon	16994.222222

	Price
body-style	convertible	hardtop	hatchback	sedan	wagon
drive-wheels
4wd	NaN	NaN	7603.000000	12647.333333	9095.750000
fwd	11595.0	8249.000000	8396.387755	9811.800000	9997.333333
rwd	23949.6	24202.714286	14337.777778	21711.833333	16994.222222

	drive-wheels	body-style	Price
0	4wd	hatchback	7603.000000
1	4wd	sedan	12647.333333
2	4wd	wagon	9095.750000
3	fwd	convertible	11595.000000
4	fwd	hardtop	8249.000000
5	fwd	hatchback	8396.387755
6	fwd	sedan	9811.800000
7	fwd	wagon	9997.333333
8	rwd	convertible	23949.600000
9	rwd	hardtop	24202.714286
10	rwd	hatchback	14337.777778
11	rwd	sedan	21711.833333
12	rwd	wagon	16994.222222

	Price
body-style	convertible	hardtop	hatchback	sedan	wagon
drive-wheels
4wd	NaN	NaN	7603.000000	12647.333333	9095.750000
fwd	11595.0	8249.000000	8396.387755	9811.800000	9997.333333
rwd	23949.6	24202.714286	14337.777778	21711.833333	16994.222222

	longitude	latitude	housing_median_age	total_rooms	total_bedrooms	population	households	median_income	median_house_value	ocean_proximity
0	-122.23	37.88	41.0	880.0	129.0	322.0	126.0	8.3252	452600.0	NEAR BAY
1	-122.22	37.86	21.0	7099.0	1106.0	2401.0	1138.0	8.3014	358500.0	NEAR BAY
2	-122.24	37.85	52.0	1467.0	190.0	496.0	177.0	7.2574	352100.0	NEAR BAY
3	-122.25	37.85	52.0	1274.0	235.0	558.0	219.0	5.6431	341300.0	NEAR BAY
4	-122.25	37.85	52.0	1627.0	280.0	565.0	259.0	3.8462	342200.0	NEAR BAY

	0	1	2	3	4	5	6	7	8	9	...	16	17	18	19	20	21	22	23	24	25
0	3	?	alfa-romero	gas	std	two	convertible	rwd	front	88.6	...	130	mpfi	3.47	2.68	9.0	111	5000	21	27	13495
1	3	?	alfa-romero	gas	std	two	convertible	rwd	front	88.6	...	130	mpfi	3.47	2.68	9.0	111	5000	21	27	16500
2	1	?	alfa-romero	gas	std	two	hatchback	rwd	front	94.5	...	152	mpfi	2.68	3.47	9.0	154	5000	19	26	16500
3	2	164	audi	gas	std	four	sedan	fwd	front	99.8	...	109	mpfi	3.19	3.40	10.0	102	5500	24	30	13950
4	2	164	audi	gas	std	four	sedan	4wd	front	99.4	...	136	mpfi	3.19	3.40	8.0	115	5500	18	22	17450

	drive-wheels	body-style	Price
0	rwd	convertible	13495.0
1	rwd	convertible	16500.0
2	rwd	hatchback	16500.0
3	fwd	sedan	13950.0
4	4wd	sedan	17450.0
...	...	...	...
200	rwd	sedan	16845.0
201	rwd	sedan	19045.0
202	rwd	sedan	21485.0
203	rwd	sedan	22470.0
204	rwd	sedan	22625.0

	housing_median_age	total_rooms	total_bedrooms	population
count	20640.000000	20640.000000	20433.000000	20640.000000
mean	28.639486	2635.763081	537.870553	1425.476744
std	12.585558	2181.615252	421.385070	1132.462122
min	1.000000	2.000000	1.000000	3.000000
25%	18.000000	1447.750000	296.000000	787.000000
50%	29.000000	2127.000000	435.000000	1166.000000
75%	37.000000	3148.000000	647.000000	1725.000000
max	52.000000	39320.000000	6445.000000	35682.000000

	PC1	PC2
0	1.009226	-0.073469
1	-0.923991	-0.085173
2	0.846904	-0.475885
3	0.844834	-0.508459
4	0.769151	-0.577098

	Area	Bedrooms	Bathrooms	Stories	Mainroad	Guestroom	Basement	Hotwaterheating	Airconditioning	Parking	Furnishingstatus	Price
0	7420	4	2	3	yes	no	no	no	yes	2	furnished	13300000
1	8960	?	4	4	yes	no	no	no	yes	3	furnished	12250000
2	?	3	2	2	yes	no	yes	no	no	2	semi-furnished	12250000
3	7500	4	2	2	yes	no	yes	no	yes	3	furnished	12215000
4	7420	4	1	2	yes	yes	yes	no	yes	2	furnished	11410000
5	7500	3	3	1	yes	no	yes	no	yes	2	semi-furnished	10850000
6	8580	4	3	4	yes	no	no	no	yes	2	semi-furnished	10150000
7	16200	5	3	?	yes	no	no	no	no	0	unfurnished	10150000
8	8100	4	1	2	yes	yes	yes	no	yes	2	furnished	9870000
9	5750	3	2	4	yes	yes	no	no	yes	1	unfurnished	9800000

	Area	Bedrooms	Bathrooms	Stories	Parking	Price
count	533.000000	535.000000	537.000000	535.000000	536.000000	5.420000e+02
mean	5155.748593	2.971963	1.286778	1.809346	0.690299	4.767167e+06
std	2167.206723	0.737669	0.503414	0.872546	0.860981	1.875564e+06
min	1650.000000	1.000000	1.000000	1.000000	0.000000	1.750000e+06
25%	3600.000000	3.000000	1.000000	1.000000	0.000000	3.430000e+06
50%	4600.000000	3.000000	1.000000	2.000000	0.000000	4.340000e+06
75%	6360.000000	3.000000	2.000000	2.000000	1.000000	5.766250e+06
max	16200.000000	6.000000	4.000000	4.000000	3.000000	1.330000e+07

	Area	Bedrooms	Bathrooms	Stories	Mainroad	Parking	Furnishingstatus	Price
0	7420.000000	4.0	2.0	3.0	yes	2.0	furnished	13300000.0
1	8960.000000	NaN	4.0	4.0	yes	3.0	furnished	12250000.0
2	5155.748593	3.0	2.0	2.0	yes	2.0	semi-furnished	12250000.0
3	7500.000000	4.0	2.0	2.0	yes	3.0	furnished	12215000.0
4	7420.000000	4.0	1.0	2.0	yes	2.0	furnished	11410000.0
...	...	...	...	...	...	...	...	...
75	4260.000000	4.0	2.0	2.0	yes	0.0	semi-furnished	6650000.0
76	5155.748593	3.0	2.0	3.0	yes	0.0	furnished	6650000.0
77	6500.000000	3.0	2.0	3.0	yes	0.0	furnished	6650000.0
78	5700.000000	3.0	1.0	1.0	yes	2.0	furnished	6650000.0
79	6000.000000	3.0	2.0	3.0	yes	0.0	furnished	6650000.0

	Area	Bedrooms	Bathrooms	Stories	Parking	Price	Mainroad_no	Mainroad_yes	Furnishingstatus_furnished	Furnishingstatus_semi-furnished	Furnishingstatus_unfurnished
0	7420.000000	4.0	2.0	3.0	2.0	13300000.0	False	True	True	False	False
1	8960.000000	3.0	4.0	4.0	3.0	12250000.0	False	True	True	False	False
2	5155.748593	3.0	2.0	2.0	2.0	12250000.0	False	True	False	True	False
3	7500.000000	4.0	2.0	2.0	3.0	12215000.0	False	True	True	False	False
4	7420.000000	4.0	1.0	2.0	2.0	11410000.0	False	True	True	False	False
...	...	...	...	...	...	...	...	...	...	...	...
540	3000.000000	2.0	1.0	1.0	2.0	1820000.0	False	True	False	False	True
541	2400.000000	3.0	1.0	1.0	0.0	1767150.0	True	False	False	True	False
542	3620.000000	2.0	1.0	1.0	0.0	1750000.0	False	True	False	False	True
543	2910.000000	3.0	1.0	1.0	0.0	1750000.0	True	False	True	False	False
544	3850.000000	3.0	1.0	2.0	0.0	1750000.0	False	True	False	False	True

	Patient ID	Age	BMI	Diagnosis	Blood Pressure
0	P0001	64	23.416480	NaN	119/66
1	P0002	49	30.539825	NaN	103/62
2	P0003	68	31.654859	Hypertension	98/70
3	P0004	22	NaN	Hypertension	117/87
4	P0005	42	NaN	Hypertension	NaN

	Patient ID	Age	BMI	Diagnosis	Blood Pressure
25	P0026	51	27.203652	Diabetes	167
26	P0027	65	23.628654	Diabetes	195
27	P0028	46	22.254053	NaN	157
28	P0029	39	28.550565	Hypertension	143
29	P0030	60	27.203652	Diabetes	185

	Patient ID	Age	BMI	Diagnosis	Blood Pressure	Age-binned
0	P0001	64	0.245243	NaN	193	Old Home Age
1	P0002	49	0.780872	NaN	163	Mature
2	P0003	68	0.864715	Hypertension	201	Old Home Age
3	P0004	22	0.530014	Hypertension	109	Adults
4	P0005	42	0.530014	Hypertension	149	Mature
5	P0006	29	0.530014	Hypertension	123	Adults
6	P0007	21	0.000000	Diabetes	107	Adults
7	P0008	51	0.114369	NaN	167	Mature
8	P0009	42	0.836924	NaN	149	Mature
9	P0010	35	1.000000	NaN	135	Adults

	normalized-losses	make
0	122.0	alfa-romero
1	122.0	alfa-romero
2	122.0	alfa-romero
3	164.0	audi
4	164.0	audi
...	...	...
200	95.0	volvo
201	95.0	volvo
202	95.0	volvo
203	95.0	volvo
204	95.0	volvo

	width	width-binned
0	0.316667	Low
1	0.316667	Low
2	0.433333	Medium
3	0.491667	Medium
4	0.508333	Medium
...	...	...
200	0.716667	High
201	0.708333	High
202	0.716667	High
203	0.716667	High
204	0.716667	High

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Assignment03.ipynb

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Exploratory Data Analysis¶

Case Study¶

Reading & Writing Data in Python¶

Exploratory Data Analysis¶

Descriptive Statistics¶

Summarize the categorical data by using value_counts( )¶

Group by Python¶

Correlation¶

Correlation Statistics¶

Model Development¶

What is a Model?¶

Linear Regression¶

Predict car price based on highway-mpg¶

Pre-Processing¶

Use Scikit Learn Library for Linear Regression¶

Multi Variable Linear Regression¶

Model Evaluation¶

Model Evaluation using Visualization¶

Problem Statement¶

Acknowledgement / Source¶

Importing Libraries¶

Loading the Dataset¶

Visualize the Data¶

Pre-Processing¶

Model¶

Silhouette (si·loo·et) Score¶

Choosing the Number of Clusters¶

Logistic Regression¶

Data Splitting¶

Evalutation Measures¶

Confusion Matrix¶

Accuracy : TP+TNTP+FN+FP+TN¶

Precision : TPTP+FP¶

Recall : TPTP+FN¶

F1-Score : 2⋅Precision⋅RecallPrecision+Recall¶

Visualizing Confusion Matrix¶

K-Means Clustering¶

Problem Statement¶

Acknowledgement / Source¶

Importing Libraries¶

Loading the Dataset¶

Visualize the Data¶

Pre-Processing¶

Model¶

Silhouette (si·loo·et) Score¶

Choosing the Number of Clusters¶

Assignment¶

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Variables

Callstack

Breakpoints

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Accuracy : $\frac{T P + T N}{T P + F N + F P + T N}$ ¶

Precision : $\frac{T P}{T P + F P}$ ¶

Recall : $\frac{T P}{T P + F N}$ ¶

F1-Score : $2 \cdot \frac{P r e c i s i o n \cdot R e c a l l}{P r e c i s i o n + R e c a l l}$ ¶